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Relaxing monotonicity in the identification of local average treatment effects

  • Huber, Martin

    ()

  • Mellace, Giovanni

    ()

In heterogeneous treatment effect models with endogeneity, the identification of the local average treatment effect (LATE) typically relies on an instrument that satisfies two conditions: (i) joint independence of the potential post-instrument variables and the instrument and (ii) monotonicity of the treatment in the instrument, see Imbens and Angrist (1994). We show that identification is still feasible when replacing monotonicity by a strictly weaker local monotonicity condition. We demonstrate that the latter allows identifying the LATEs on the (i) compliers (whose treatment reacts to the instrument in the intended way), (ii) defiers (who react counter-intuitively), and (iii) both populations jointly. Furthermore, (i) and (iii) coincides with standard LATE if monotonicity holds. We also present an application to the quarter of birth instrument of Angrist and Krueger (1991).

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File URL: http://www1.vwa.unisg.ch/RePEc/usg/econwp/EWP-1212.pdf
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Paper provided by University of St. Gallen, School of Economics and Political Science in its series Economics Working Paper Series with number 1212.

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Length: 48 pages
Date of creation: May 2012
Date of revision:
Handle: RePEc:usg:econwp:2012:12
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  1. Newey, W.K., 1989. "The Asymptotic Variance Of Semiparametric Estimotors," Papers 346, Princeton, Department of Economics - Econometric Research Program.
  2. Frolich, Markus, 2007. "Nonparametric IV estimation of local average treatment effects with covariates," Journal of Econometrics, Elsevier, vol. 139(1), pages 35-75, July.
  3. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
  4. Toru Kitagawa, 2009. "Identification region of the potential outcome distributions under instrument independence," CeMMAP working papers CWP30/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Klein, T.J., 2008. "Heterogeneous Treatment Effects : Instrumental Variables Without Monotonicity?," Discussion Paper 2008-45, Tilburg University, Center for Economic Research.
  6. Imbens, Guido W & Rubin, Donald B, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 555-74, October.
  7. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  8. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics 2167, London School of Economics and Political Science, LSE Library.
  9. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages S2-S18, 09.
  10. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  11. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  12. Card, David, 1999. "The causal effect of education on earnings," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 30, pages 1801-1863 Elsevier.
  13. Rashmi Barua & Kevin Lang, 2009. "School Entry, Educational Attainment and Quarter of Birth: A Cautionary Tale of LATE," NBER Working Papers 15236, National Bureau of Economic Research, Inc.
  14. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
  15. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  16. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355, April.
  17. Joshua D. Angrist & Alan B. Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," NBER Working Papers 3572, National Bureau of Economic Research, Inc.
  18. Martin Huber & Giovanni Mellace, 2010. "Sharp IV bounds on average treatment effects under endogeneity and noncompliance," University of St. Gallen Department of Economics working paper series 2010 2010-31, Department of Economics, University of St. Gallen.
  19. Dai, J. & Sperlich, S., 2010. "Simple and effective boundary correction for kernel densities and regression with an application to the world income and Engel curve estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2487-2497, November.
  20. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
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